For m∈N, we let P(G,m) be the chromatic polynomial of the graph G; that is, P(G,m) is equal to the number of proper m-colorings of G. It can be shown that P(G,m) is a polynomial in m of degree |V(G)| (see [11])
One can find cographs discussed in a variety of places (e.g. [5], [12], [26]). They are a well structured and relatively simple class. Indeed, difficult problems such as maximum clique, maximum independent set, chromatic number, minimum clique cover, and Hamiltonicity are polynomial when...
In experiments the quantum wires considered in the previous chapter are often combined into more complicated structures. This opens the way to numerous interesting physical effects, however, from the theoretical point of view such systems are not easy to
Functions & Graphs
For readers interested in (P5, H )-free graphs with polynomial binding functions, we refer more results to [16, 17] However, the question of determinating a polynomial binding function for (P5, H )- free graphs is still open for lots of H with small order. Chudnovsky and Sivaraman [5...
The set of all edges in the graph is denoted as E. Finally, the weight function, W : E ! Rþ, assigns a non-negative real weight to each edge in E. For instance, the weight function could simply encode the physical distance between voxels. Alternate weight functions could encode hop...
For convex functions, it is possible to connect any two points with a straight line. This feature is also (partially) captured by the HVG. If v is contained in a convex part of the related time series, there is a high degree of intervisibility among the neighbor vertices to which v is...
4. Cubic Polynomial Parent Function Cubic functionsareodd functions. The parent is:f(x) = x3. The cubic parent function isstrictly increasing, which basically means it’s always headed upwards. Graph of the cubic parent function f(x) = x3. ...
Also, the four classes have polynomial time recognition algorithms, so one could conjecture that so does the class of wheel-free graphs. But it is proved in [5] that it is NP-hard to recognize them. All this suggest that possibly, no structural description of wheel-free graphs exists. ...
A graphic drawing apparatus divides an xy plane corresponding to a two-dimensional display region into plural display units. While one of two variables of the polynomial f(x, y) is fixed, a univeriate